There's a 10-square limit on the fireplaces, I think? If you've got a very large room, you'll need more than one.
You won't need one in the bath, as long as they're only going in there to get clean and get out - they're fine while they're in the bath. My Sim gets a little chilled when she bathes her toddler, but nothing life-threatening. And they don't need the fireplace once they're in bed, so if they're only using the bedrooms to sleep, they won't need a fireplace. Also, if you upgrade it to autolight, it will go out when they get into bed or leave the room.
Speaking of upgrades, I don't let my Sims use a fireplace until they have enough handiness (level 6, I think) to upgrade the fireplace with fire guard. Otherwise, you will have it catching fire. Frequently. (Even with fire guard, it can still cause a fire - my Sim kid decided to play the violin one square from the fireplace and ended up a bit toasted. Fortunately, her mother was able to extinguish her, but the violin was a loss.) Make sure the fireplace has brick or stone tiles around it, and that chairs are at least two squares back.